What is the length of the arc given that the radius is 12cm and the central angle is 4š/3? Round your answer to the nearest tenth.
To find the length of the arc, you can use the formula:
Arc Length = (Central Angle / 2š) * Circumference
First, let's find the circumference of the circle using the formula:
Circumference = 2š * Radius
Given that the radius is 12 cm, we can substitute this value into the formula:
Circumference = 2š * 12
Circumference = 24š
Now, we can substitute the values into the formula for arc length:
Arc Length = (4š/3 / 2š) * 24š
Arc Length = (4š/3) * (24š / 2š)
Arc Length = (4š/3) * 12
Arc Length = 16š
To round the answer to the nearest tenth, we can substitute the value of š with approximately 3.14:
Arc Length ā 16 * 3.14
Arc Length ā 50.24 cm
Therefore, the length of the arc is approximately 50.24 cm when rounded to the nearest tenth.